Here you find the prototype implementation for Maple of the Algorithms presented in the paper

"Quasi-stable and Borel-fixed ideals of a Hilbert scheme" (accepted for publication on Applicable Algebra in Engineering, Communication and Computing)

and several examples.

The computations for the examples of the paper are contained in files

6t-3n3.mw

6t-3n3QS.mw

14n2.mw

Warning: in all procedures and examples, we consider x_n>....>x_0.

File MonomialIdeals.txt contains general procedures to handle monomial ideals. Requires Maple package Groebner.

File BorelFixed.txt contains procedures to test whether a monomial ideal is Borel-fixed, depending on the characteristic of the coefficient field. Requires MonomialIdeals.txt

File AlgoQStablePBorel.txt contains the procedures to compute the complete list of quasi-stable ideals and of p-Borel ideals with a given Hilbert polynomial. Requires MonomialIdeals.txt

The name of the Maple files are of type "polynomial-n-number.mw" where "polynomial" is an admissible Hilbert polynomial and "number" is the index of the biggest variable of the considered polynomial ring. To run the examples on your computer you need to download the example file and also to save in the same folder the files "name.txt", which contain the procedures. At the begininnig of each file you find the command read "name.txt", which look for the needed procedure file. If you want to know what procedure "UnkonownProcedure" does, just write in one of the maple files "Describe(UnknownProcedure)" to obtain a description of input and output.

UPDATE JUNE 2015:

procedure Remove (and PRemove) has been improved adding a further parameter (a term) in order to avoid to compute several times the same ideal, similarly to what is done in the paper by P. Lella (arXiv:1205.0456 [cs.SC], published on the Proceedings of Issac 2012).

Further, the procedures are now faster, by avoiding to compute saturations and truncations at the following recursive call of the main algorithms. As a consequence, the output of the two main algorithms (QuasiStable and PBorel) are now truncation ideals, and no more saturated ideals. Thanks for the suggestions about this to Mario Albert and Werner Seiler